Bose-Einstein condensation in a one-dimensional interacting system due to power-law trapping potentials

TL;DR

This paper investigates the occurrence of Bose-Einstein condensation in a one-dimensional interacting Bose gas confined by power-law potentials with exponent less than two, using the Gross-Pitaevskii equation and semi-classical model.

Contribution

It demonstrates the possibility of Bose-Einstein condensation in 1D systems with specific power-law trapping potentials, highlighting conditions for phase transition in weakly interacting gases.

Findings

Significant condensate fraction observed at low temperatures.

Condensation occurs for finite particle numbers in weakly interacting systems.

Calculated thermodynamic properties vary with interaction strength and potential parameters.

Abstract

We examine the possibility of Bose-Einstein condensation in one-dimensional interacting Bose gas subjected to confining potentials of the form $V_{\rm ext}(x)=V_0(|x|/a)^\gamma$, in which $\gamma < 2$, by solving the Gross-Pitaevskii equation within the semi-classical two-fluid model. The condensate fraction, chemical potential, ground state energy, and specific heat of the system are calculated for various values of interaction strengths. Our results show that a significant fraction of the particles is in the lowest energy state for finite number of particles at low temperature indicating a phase transition for weakly interacting systems.